How Do You Calculate Path-Length Differences in Two-Source Interference?

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The discussion focuses on calculating path-length differences at specific points (A, C, and D) in a two-source interference problem. Users initially attempted various numerical answers in terms of wavelength (λ) but found them incorrect. Eventually, one participant successfully derived the correct values by analyzing the provided diagrams. The importance of visual representation in solving such problems is emphasized, as it aids in understanding the path-length differences. The conversation highlights the iterative process of problem-solving in physics.
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Homework Statement



1014010E.jpg

http://session.masteringphysics.com/problemAsset/1014010/14/1014010E.jpg

What are the path-length differences at Points A, C, and D
(respectively, ΔdA, ΔdC, ΔdD)?

Enter your answers numerically in terms of lambda λ

Homework Equations



Does this require an equation? I figured it was pictorial

1014010D.jpg

http://session.masteringphysics.com/problemAsset/1014010/14/1014010D.jpg

The Attempt at a Solution



I looked at the picture and tried the following, which were all incorrect:

3.5, 2.5, 2
3, 2, 1.5
 
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Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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